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Title: 2006 World Championship Post by 99of9 on Nov 13th, 2005, 8:49pm Looks like it's time for a new thread so we can discuss the guts of the tourney as they spill. Having seen the pairings, I've appreciated for the first time the serious strength in this year's championship. We'll either see some big upsets in round 1, or some very big clashes already in round 2. If things go according to ratings, 2005-world-champ plays 2004&2005-third-place in round 2 of a 7 round tourney!?! Unheard of. And it's not just because Omar is underrated... nearly all the round 2 clashes look set to be almost as big. (Even round 1 has naveed vs robinson and jdb vs Ryan ...) So, having seen the depth of the field, I think this year's tourney is really up for grabs. I could readily imagine any of 10 players actually winning the comp! And well done to everyone who entered, it's really great to see even some beginners throwing in their hand. I think participating in something like this will be a great experience for all of us. |
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Title: Re: 2006 World Championship Post by Ryan_Cable on Nov 14th, 2005, 2:50am The tournament has 16 players: 1 Fritzlein 2273 2 99of9 2142 3 Ryan_Cable 2105 4 PMertens 2045 5 Adanac 2039 6 robinson 2026 7 Belbo 2009 8 omar 1860 9 Paul 1827 10 BlackKnight 1818 11 naveed 1678 12 megamau 1651 13 grey_0x2A 1609 14 jdb 1584 15 acheron 1386 16 MrBrain 1369 Median 1843.5 Mean 1838.8 StDev 271.2 I wrote a python script to simulate the tournament and estimate people’s chances. I estimated people’s true-rating by taking a Gaussian distribution about their rating. For each case below, I ran the simulation for 100,000 trials, which took about 100s per case. I am not sure exactly what the expected error of these simulations is, but I would guess it is about 1/Sqrt(100000) ~= 0.00316 StDev 0 (true-rating = rating): 1 Fritzlein 0.65264 2 99of9 0.16353 3 Ryan_Cable 0.08959 4 PMertens 0.03478 5 Adanac 0.02731 6 robinson 0.01959 7 Belbo 0.01170 8 omar 0.00049 9 Paul 0.00021 10 BlackKnight 0.00015 11 naveed 0.00001 12 megamau 0 13 grey_0x2A 0 14 jdb 0 15 acheron 0 16 MrBrain 0 StDev 50: 1 Fritzlein 0.61176 2 99of9 0.17013 3 Ryan_Cable 0.09942 4 PMertens 0.03888 5 Adanac 0.03592 6 robinson 0.02624 7 Belbo 0.01601 8 omar 0.00099 9 Paul 0.00044 10 BlackKnight 0.00021 11 naveed 0 12 megamau 0 13 grey_0x2A 0 14 jdb 0 15 acheron 0 16 MrBrain 0 StDev 100: 1 Fritzlein 0.52828 2 99of9 0.17758 3 Ryan_Cable 0.11514 4 PMertens 0.05532 5 Adanac 0.05059 6 robinson 0.03991 7 Belbo 0.02780 8 omar 0.00286 9 Paul 0.00148 10 BlackKnight 0.00097 11 naveed 0.00003 12 megamau 0.00002 13 grey_0x2A 0 14 jdb 0.00002 15 acheron 0 16 MrBrain 0 StDev 200: 1 Fritzlein 0.37288 2 99of9 0.17004 3 Ryan_Cable 0.12907 4 PMertens 0.08139 5 Adanac 0.07862 6 robinson 0.06899 7 Belbo 0.05777 8 omar 0.01611 9 Paul 0.01110 10 BlackKnight 0.00949 11 naveed 0.00205 12 megamau 0.00127 13 grey_0x2A 0.00070 14 jdb 0.00045 15 acheron 0.00006 16 MrBrain 0.00001 I also tested the effect of lowering my rating to a more realistic 1800, but keeping the ranking the same. StDev 0: 1 Fritzlein 0.68330 2 99of9 0.19008 3 Ryan_Cable 0.00063 4 PMertens 0.04343 5 Adanac 0.03471 6 robinson 0.02959 7 Belbo 0.01695 8 omar 0.00077 9 Paul 0.00036 10 BlackKnight 0.00018 11 naveed 0 12 megamau 0 13 grey_0x2A 0 14 jdb 0 15 acheron 0 16 MrBrain 0 StDev 50 (I think this is probably closest to the actual odds.): 1 Fritzlein 0.64724 2 99of9 0.19530 3 Ryan_Cable 0.00125 4 PMertens 0.05255 5 Adanac 0.04239 6 robinson 0.03649 7 Belbo 0.02210 8 omar 0.00137 9 Paul 0.00085 10 BlackKnight 0.00042 11 naveed 0.00002 12 megamau 0.00001 13 grey_0x2A 0 14 jdb 0.00001 15 acheron 0 16 MrBrain 0 StDev 100: 1 Fritzlein 0.56945 2 99of9 0.20130 3 Ryan_Cable 0.00285 4 PMertens 0.07013 5 Adanac 0.05938 6 robinson 0.05246 7 Belbo 0.03601 8 omar 0.00431 9 Paul 0.00242 10 BlackKnight 0.00138 11 naveed 0.00016 12 megamau 0.00010 13 grey_0x2A 0.00001 14 jdb 0.00004 15 acheron 0 16 MrBrain 0 StDev 200: 1 Fritzlein 0.40832 2 99of9 0.19373 3 Ryan_Cable 0.01350 4 PMertens 0.09553 5 Adanac 0.08964 6 robinson 0.08267 7 Belbo 0.06632 8 omar 0.01866 9 Paul 0.01383 10 BlackKnight 0.01139 11 naveed 0.00257 12 megamau 0.00180 13 grey_0x2A 0.00111 14 jdb 0.00087 15 acheron 0.00003 16 MrBrain 0.00003 Then, I tested the effect of lowering my rating to 1800, and changing the rankings to match. StDev 0: 1 Fritzlein 0.68136 2 99of9 0.19066 3 PMertens 0.04616 4 Adanac 0.03802 5 robinson 0.02455 6 Belbo 0.01785 7 omar 0.00072 8 Paul 0.00033 9 BlackKnight 0.00020 10 Ryan_Cable 0.00014 11 naveed 0.00001 12 megamau 0 13 grey_0x2A 0 14 jdb 0 15 acheron 0 16 MrBrain 0 StDev 50: 1 Fritzlein 0.64623 2 99of9 0.19603 3 PMertens 0.05494 4 Adanac 0.04499 5 robinson 0.03186 6 Belbo 0.02322 7 omar 0.00130 8 Paul 0.00073 9 BlackKnight 0.00045 10 Ryan_Cable 0.00021 11 naveed 0.00004 12 megamau 0 13 grey_0x2A 0 14 jdb 0 15 acheron 0 16 MrBrain 0 StDev 100: 1 Fritzlein 0.56895 2 99of9 0.20362 3 PMertens 0.07017 4 Adanac 0.06153 5 robinson 0.04906 6 Belbo 0.03713 7 omar 0.00402 8 Paul 0.00236 9 BlackKnight 0.00184 10 Ryan_Cable 0.00116 11 naveed 0.00007 12 megamau 0.00007 13 grey_0x2A 0 14 jdb 0.00002 15 acheron 0 16 MrBrain 0 StDev 200: 1 Fritzlein 0.40815 2 99of9 0.19326 3 PMertens 0.09713 4 Adanac 0.08911 5 robinson 0.08172 6 Belbo 0.06930 7 omar 0.01908 8 Paul 0.01497 9 BlackKnight 0.01230 10 Ryan_Cable 0.00954 11 naveed 0.00226 12 megamau 0.00152 13 grey_0x2A 0.00089 14 jdb 0.00067 15 acheron 0.00009 16 MrBrain 0.00001 Multiplicatively the effect of my being overrated is as follows: I, robinson, omar, and Paul are notably improved. Adanac, PMertens, and Belbo are notably harmed. Others mostly vanish into the noise, though I expect jdb is substantially improved. The absolute sum of the additive effect of my being overrated is about 0.015 for all cases. StDev 0: 1 Fritzlein 1.00284 2 99of9 0.99695 3 PMertens 0.94085 4 Adanac 0.91294 5 robinson 1.20529 6 Belbo 0.94957 7 omar 1.06944 8 Paul 1.09090 9 BlackKnight 0.9 10 Ryan_Cable 4.5 11 naveed 0 12 megamau ? 13 grey_0x2A ? 14 jdb ? 15 acheron ? 16 MrBrain ? StDev 50: 1 Fritzlein 1.00156 2 99of9 0.99627 3 PMertens 0.95649 4 Adanac 0.94220 5 robinson 1.14532 6 Belbo 0.95176 7 omar 1.05384 8 Paul 1.16438 9 BlackKnight 0.93333 10 Ryan_Cable 5.95238 11 naveed 0.5 12 megamau ? 13 grey_0x2A ? 14 jdb ? 15 acheron ? 16 MrBrain ? StDev 100: 1 Fritzlein 1.00087 2 99of9 0.98860 3 PMertens 0.99942 4 Adanac 0.96505 5 robinson 1.06930 6 Belbo 0.96983 7 omar 1.07213 8 Paul 1.02542 9 BlackKnight 0.75 10 Ryan_Cable 2.45689 11 naveed 2.28571 12 megamau 1.42857 13 grey_0x2A ? 14 jdb 2 15 acheron ? 16 MrBrain ? StDev 200: 1 Fritzlein 1.00041 2 99of9 1.00243 3 PMertens 0.98352 4 Adanac 1.00594 5 robinson 1.01162 6 Belbo 0.95699 7 omar 0.97798 8 Paul 0.92384 9 BlackKnight 0.92601 10 Ryan_Cable 1.41509 11 naveed 1.13716 12 megamau 1.18421 13 grey_0x2A 1.24719 14 jdb 1.29850 15 acheron 0.33333 16 MrBrain 3 If anyone is interested in a copy of my script I would be happy to provide it, but you can probably do the same things with Omar’s scripts. I will try to post new odds after each round. |
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Title: Re: 2006 World Championship Post by PMertens on Nov 14th, 2005, 3:13am I really do not feel harmed by your rating :-D |
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Title: Re: 2006 World Championship Post by Ryan_Cable on Nov 14th, 2005, 3:53am That is good to hear. :-) I do think we should improve the rating system before the next WC. There was a big discussion of this a while back, but nothing was decided. |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 14th, 2005, 8:08am I think Omar is still committed to improving the rating system, but he got distracted discussing tournament formats. I'm glad he did, because (IMHO) floating double elimination with inaccurate seeding is much better than single elimination with accurate seeding. The above numbers substantiate this somewhat. Looking forward, I think improved ratings are still important, but a greater priority should be server stability and capacity. And of course even before that it is important that the computer championship, challenge match, and postal championship run smoothly again this year. |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 14th, 2005, 8:29am With as many strong players as there are in this tourney, it is really hard for me to believe that I have a 60% or better shot of winning the whole thing. When the possibility of error is introduced, I feel obliged to point out that my true strength is much more likely to be 2170 than 2370. Is this just my psychological hangup that I have trouble believing in myself, or do other people also feel that the World Championship is more open than the ratings-based simulation suggests? |
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Title: Re: 2006 World Championship Post by Adanac on Nov 14th, 2005, 10:18am on 11/14/05 at 08:29:08, Fritzlein wrote:
Overconfidence has been the downfall of many favourites in sports, elections, etc. so your "psychological hangup" may be more of an asset than anything. As long as you're not reading the newspaper during your games or anything, I'd give you at least a 50% shot at 1st place :) |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 14th, 2005, 3:05pm on 11/14/05 at 02:50:16, Ryan_Cable wrote:
When you calculate ratios, it may seem like the system has a major flaw: you have doubled your odds of winning or more than doubled them by pumping up your rating to get a better seed. However, if the effect in absolute terms is to raise your chances of becoming World Champion from 0.1% to 0.2%, I don't think anyone will begrudge you the extra one-in-a-thousand chance. As for other people being helped or hurt by an inaccuracy in your rating, I think there are just too many inaccuracies in everyone's ratings to make that a useful calculation. Maybe Omar is slightly harmed by your inflated rating, but would have been slightly helped by your inflated rating if Naveed's rating hadn't been deflated, except if a person rated 1477 entered the tournament at the last minute to create a first-round bye... It makes me think of a football game which ends up 33-31, and everyone talks only about the missed field goal in the final seconds. In such a close game you could change any one of fifty different plays and reverse the overall outcome. It's a bit silly to focus on only one variable in a huge, unstable system which can't be accurately measured or predicted in the first place. |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 14th, 2005, 3:13pm on 11/14/05 at 10:18:37, Adanac wrote:
That's a nice way to put it. Thank you. Usually sports commentators say things like, "He's playing with confidence now," as if a lack of confidence were responsible for all of some athlete's mistakes up to that point. |
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Title: Re: 2006 World Championship Post by Ryan_Cable on Nov 14th, 2005, 8:33pm on 11/14/05 at 08:08:05, Fritzlein wrote:
That is definitely true, in a single elimination tournament the chance of you or 99of9 winning drops ~7% (additively). Going to floating triple elimination would add another 5% to 7% to your combined chances, potentially leaving as little as 4% for the field. on 11/14/05 at 08:29:08, Fritzlein wrote:
The thing to remember is that this format was specifically selected to maximize the probability of picking the player with the highest true-rating. I am 99%+ confident that person is Fritzlein or 99of9 and 75% confident it is Fritzlein. I had planned to do simulations with more rating adjustments after the first round, but I will go ahead and do it now. With Fritzlein dropped 50 points and myself at 1800: (Ignore the periods, they are just a hack to get around the fact that the forum software will not display more than 5 spaces in a row, and I am to much lazy to redo everything with tables.) StDev 0: 1 Fritzlein 0.57179 2 99of9 . 0.24952 3 Ryan_Cable 0.00108 4 PMertens 0.06147 5 Adanac . 0.04780 6 robinson 0.04197 7 Belbo . 0.02432 8 omar . 0.00122 9 Paul . 0.00049 10 BlackKnight 0.00032 11 naveed . 0.00001 12 megamau 0 13 grey_0x2A 0 14 jdb . 0.00001 15 acheron 0 16 MrBrain 0 StDev 50: 1 Fritzlein 0.54342 2 99of9 . 0.24756 3 Ryan_Cable 0.00149 4 PMertens 0.06912 5 Adanac . 0.05657 6 robinson 0.04755 7 Belbo . 0.03045 8 omar . 0.00216 9 Paul . 0.00104 10 BlackKnight 0.00058 11 naveed . 0.00004 12 megamau 0.00002 13 grey_0x2A 0 14 jdb . 0 15 acheron 0 16 MrBrain 0 StDev 100: 1 Fritzlein 0.47359 2 99of9 . 0.24228 3 Ryan_Cable 0.00355 4 PMertens 0.08405 5 Adanac . 0.07460 6 robinson 0.06607 7 Belbo . 0.04462 8 omar . 0.00572 9 Paul . 0.00320 10 BlackKnight 0.00211 11 naveed . 0.00012 12 megamau 0.00006 13 grey_0x2A 0.00001 14 jdb . 0.00002 15 acheron 0 16 MrBrain 0 With Fritzlein dropped 100 points and myself at 1800: StDev 0: 1 Fritzlein 0.45215 2 99of9 . 0.31091 3 Ryan_Cable 0.00142 4 PMertens 0.07898 5 Adanac . 0.06333 6 robinson 0.05820 7 Belbo . 0.03227 8 omar . 0.00175 9 Paul . 0.00059 10 BlackKnight 0.00038 11 naveed . 0.00001 12 megamau 0.00001 13 grey_0x2A 0 14 jdb . 0 15 acheron 0 16 MrBrain 0 StDev 50: 1 Fritzlein 0.42771 2 99of9 . 0.30430 3 Ryan_Cable 0.00203 4 PMertens 0.08492 5 Adanac . 0.07194 6 robinson 0.06280 7 Belbo . 0.04085 8 omar . 0.00304 9 Paul . 0.00160 10 BlackKnight 0.00077 11 naveed . 0.00002 12 megamau 0.00002 13 grey_0x2A 0 14 jdb . 0 15 acheron 0 16 MrBrain 0 StDev 100: 1 Fritzlein 0.37609 2 99of9 . 0.28095 3 Ryan_Cable 0.00461 4 PMertens 0.10079 5 Adanac . 0.08941 6 robinson 0.07849 7 Belbo . 0.05569 8 omar . 0.00723 9 Paul . 0.00393 10 BlackKnight 0.00251 11 naveed . 0.00013 12 megamau 0.00010 13 grey_0x2A 0.00004 14 jdb . 0.00003 15 acheron 0 16 MrBrain 0 Now let’s look at Fritzlein’s record and see how ridiculous it is to think he is 100 points overrated: Name . Record Win Rate Predicted Win Rate 99of9 . 6-9 0.40 . 0.680 Ryan_Cable 1-0 1 . 0.938 (at 1800) PMertens 17-5 0.7727 . 0.788 Adanac . 11-1 0.9167 . 0.794 robinson 19-3 0.8636 . 0.806 Belbo . 8-1 0.8889 . 0.820 omar . 8-0 1 . 0.915 Except for 99of9, Fritzlein performs above expectations against everyone but PMertens, where he performs as expected (and the record against PMertens is somewhat distorted by browser crash timeouts on both sides). The record between 99of9 and Fritzlein is interesting but tragically small. If the games before 2005 are removed (in 2004, 99of9 had the top rating and Fritzlein just joined in August), the record is 6-5, 0.5455 in favor of 99of9. However, if we count only interactive games of 30s+ per move in 2005, the record is 5-1 in favor of 99of9, 0.833. Clearly, if Fritzlein has an Achilles’ heal, it is 99of9. If the World Championship were going to be decided by a match (say best of 9), 99of9 might even be a slight favorite. Now let’s look at 99of9’s record: Name . Record Win Rate Predicted Win Rate Fritzlein 9-6 0.60 . 0.320 Ryan_Cable 3-0 1 . 0.877 (at 1800) PMertens 14-1 0.9333 . 0.636 Adanac . 1-4 0.20 . 0.644 robinson 11-6 0.6471 . 0.661 Belbo . 28-7 0.80 . 0.683 omar . 9-4 0.6923 . 0.835 (Corrected: I have put 99of9 25 points less underrated, see 99of9's post below) The games against Adanac were four blitz games and one postal game. Otherwise, 99of9 outperforms against everyone except robinson where he performs as expected and the underrated omar where he performs below expectations. I think 99of9 is probably 50 to 75 points underrated relative to the population under study. If 50 to 75 points were added to 99of9’s rating, I think Fritzlein would be more likely to be underrated than overrated relative to the population under study. With Fritzlein unchanged and myself at 1800, I raised 99of9 50 points. And just to make things as accurate as possible, I raised omar 100 points as well: StDev 0: 1 Fritzlein 0.61057 2 99of9 . 0.27491 3 Ryan_Cable 0.00059 4 PMertens 0.03841 5 Adanac . 0.03085 6 robinson 0.02558 7 Belbo . 0.01395 8 omar . 0.00479 9 Paul . 0.00024 10 BlackKnight 0.00011 11 naveed . 0 12 megamau 0 13 grey_0x2A 0 14 jdb . 0 15 acheron 0 16 MrBrain 0 StDev 50: 1 Fritzlein 0.58171 2 99of9 . 0.27857 3 Ryan_Cable 0.00075 4 PMertens 0.04451 5 Adanac . 0.03637 6 robinson 0.03208 7 Belbo . 0.01831 8 omar . 0.00686 9 Paul . 0.00053 10 BlackKnight 0.00028 11 naveed . 0.00003 12 megamau 0 13 grey_0x2A 0 14 jdb . 0 15 acheron 0 16 MrBrain 0 StDev 100: 1 Fritzlein 0.51385 2 99of9 . 0.27358 3 Ryan_Cable 0.00247 4 PMertens 0.06003 5 Adanac . 0.05275 6 robinson 0.04632 7 Belbo . 0.03245 8 omar . 0.01555 9 Paul . 0.00172 10 BlackKnight 0.00114 11 naveed . 0.00006 12 megamau 0.00001 13 grey_0x2A 0.00004 14 jdb . 0.00003 15 acheron 0 16 MrBrain 0 With Fritzlein unchanged, myself at 1800, and omar raised 100, I raised 99of9 75 points: StDev 0: 1 Fritzlein 0.57088 2 99of9 . 0.32846 3 Ryan_Cable 0.00046 4 PMertens 0.03416 5 Adanac . 0.02654 6 robinson 0.02273 7 Belbo . 0.01222 8 omar . 0.00420 9 Paul . 0.00024 10 BlackKnight 0.00010 11 naveed . 0 12 megamau 0.00001 13 grey_0x2A 0 14 jdb . 0 15 acheron 0 16 MrBrain 0 StDev 50: 1 Fritzlein 0.54817 2 99of9 . 0.32487 3 Ryan_Cable 0.00087 4 PMertens 0.04079 5 Adanac . 0.03337 6 robinson 0.02801 7 Belbo . 0.01666 8 omar . 0.00668 9 Paul . 0.00035 10 BlackKnight 0.00023 11 naveed . 0 12 megamau 0 13 grey_0x2A 0 14 jdb . 0 15 acheron 0 16 MrBrain 0 StDev 100: 1 Fritzlein 0.49273 2 99of9 . 0.31409 3 Ryan_Cable 0.00212 4 PMertens 0.05623 5 Adanac . 0.04735 6 robinson 0.04284 7 Belbo . 0.02836 8 omar . 0.01362 9 Paul . 0.00147 10 BlackKnight 0.00108 11 naveed . 0.00005 12 megamau 0.00003 13 grey_0x2A 0.00001 14 jdb . 0.00002 15 acheron 0 16 MrBrain 0 With Fritzlein unchanged, myself at 1800, and omar raised 100, I raised 99of9 100 points: StDev 0: 1 Fritzlein 0.52674 2 99of9 . 0.38388 3 Ryan_Cable 0.00034 4 PMertens 0.03079 5 Adanac . 0.02366 6 robinson 0.02025 7 Belbo . 0.01038 8 omar . 0.00376 9 Paul . 0.00012 10 BlackKnight 0.00007 11 naveed . 0.00001 12 megamau 0 13 grey_0x2A 0 14 jdb . 0 15 acheron 0 16 MrBrain 0 StDev 50: 1 Fritzlein 0.51155 2 99of9 . 0.37558 3 Ryan_Cable 0.00070 4 PMertens 0.03623 5 Adanac . 0.02966 6 robinson 0.02538 7 Belbo . 0.01512 8 omar . 0.00524 9 Paul . 0.00032 10 BlackKnight 0.00019 11 naveed . 0.00003 12 megamau 0 13 grey_0x2A 0 14 jdb . 0 15 acheron 0 16 MrBrain 0 StDev 100: 1 Fritzlein 0.46331 2 99of9 . 0.35655 3 Ryan_Cable 0.00172 4 PMertens 0.05241 5 Adanac . 0.04380 6 robinson 0.03999 7 Belbo . 0.02748 8 omar . 0.01233 9 Paul . 0.00128 10 BlackKnight 0.00103 11 naveed . 0.00004 12 megamau 0.00004 13 grey_0x2A 0.00001 14 jdb . 0.00001 15 acheron 0 16 MrBrain 0 After some reflection, I think most of the statistical information about this tournament can be summed up in a few observations: For either Fritzlein or 99of9 to win the tournament, one almost certainly must beat the other at least once. To win, Fritzlein will probably have to beat 99of9 twice. To win, 99of9 is notably more likely to have to beat Fritzlein twice. For anyone else to win, that person will almost certainly need a total of at least 2 wins against Fritzlein and 99of9, and will probably need a total of at least 3 wins against them. I believe there is actually a significant chance that this person would have to beat Fritzlein and 99of9 twice each, a truly amazing feat! If either Fritzlein or 99of9 is undefeated after round 4, he will have a ~70% chance of winning the tournament (needing to go 2 out of 3 against equal or weaker opponents). If someone else is undefeated after round 4 (and Fritzlein and 99of9 are still in the tournament), he will have a ~30% chance of winning the tournament (needing to go 2 out of 3 against opponents that are probably stronger). (Slightly changed, see 99of9's post below and the correction above) Based on this, I think the odds for the tournament are roughly Fritzlein: 57%, 99of9: 37%, field: 6%. Note that all of my simulations give the field ~10% or better; I humbly disagree. Alone, Fritzlein and 99of9 are beatable, but together, in a floating double elimination tournament, they cover the road to the Championship with nearly impenetrable interlocking fires. Arguably the greatest advantage Fritzlein and 99of9 have is that they only have to face one titan, while everyone else has to face two. ;-) |
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Title: Re: 2006 World Championship Post by 99of9 on Nov 14th, 2005, 9:48pm on 11/14/05 at 20:33:14, Ryan_Cable wrote:
But of course you mean "true rating in 90-120 sec games". I am significantly weaker at postal than at 45s. Most of the interactive human games played on the server are 45s-60s, smack bang in the middle of my competency, my psychological tricks sometimes work. So I think that in a 90/120 tourney I am probably not underrated. On the contrary I think Fritz's postal record demonstrates that he is an arimaa player like no other. But in a tourney, you never know what might happen - for all we know, someone might have prepared a never-before-imagined opening that leaves us all for dead ;-). Quote:
I agree with you, it's quite possible that he is underrated. We will not truly know that until someone comes along that is rated similarly to him. It's very hard to rise when you already way off the scale, because something as little as a browser crash can set you back 30 points. Quote:
That is my fault. As you can see from his table Fritz has a much higher work-rate than me. In my table, the quantity of games vs Fritz looks perfectly normal! Quote:
Perhaps I should start a rebel "Classical World Arimaa Champion" system like in chess :-). I think there's a little truth in what you say about me being his possible Achilles heel. I'm lucky that despite us all cajoling him to play, one of my Achilles heels (blue22) is not in the WC (One other is Adanac as you rightly point out, and one other is Omar - see below). Quote:
I've corrected the Belbo and omar entries - I think you cut and pasted from Fritz's record for them. One of the games against PMertens was the Lose-Arimaa variant :-). I think I may have been his Achilles heel so far. Many of the games against Belbo were when he was learning. As you can see I underperform against Omar, but that's because he is underrated in your expectation calculation. Quote:
I doubt it, especially at this longer time control. Remember last year I was knocked out in round 1 by naveed. Quote:
I have great hopes for Omar and PMertens on Fritz's side of the draw :-). Quote:
I think unexpected surprises are even more likely around tourney time, so I'd give the "field" about 20%, Fritz 50%, and me 30%. Quote:
I just wanted to quote this :-) |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 14th, 2005, 11:27pm on 11/14/05 at 21:48:04, 99of9 wrote:
I guess if I had to set down odds where I would take any side of the bet, this is what I would say too. If Ryan would lay me 19 to 1 odds against the fourteen, I'd take the field any day. Of course then I would try to make sure I lost the bet... ;) |
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Title: Re: 2006 World Championship Post by Ryan_Cable on Nov 15th, 2005, 2:17am on 11/14/05 at 21:48:04, 99of9 wrote:
Thanks, I made the corrections you noted in my post above. Cutting and pasting from three different windows, while running simulations, with 10+ windows open is a bit tricky. ;-) It slightly changed my guesstimate of the odds to roughly Fritzlein: 57%, 99of9: 37%, field: 6%. on 11/14/05 at 21:48:04, 99of9 wrote:
In a tournament this big, there will definitely be upsets. However, due to the design of the FDE, there needs to be several upsets for a non-titan to win. This seems to be particularly true for the 16 player FDE. Look at Fritzlein’s description of the tournament endgame in the World Championship format for 2006 thread: http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1124140602;start=15 As seeds 1 and 2, I believe that 99of9 and Fritzlein can potentially play each other at only two specific times: The first opportunity is in round 4 in a critical battle to be the last remaining undefeated player. The only other time they can meet is at the end of the tournament playing for the win. If the round 4 game does come to pass, the tournament will almost certainly be won by a titan, because it implies that only 3 non-titans will survive round 4, and further implies that at most 2, and probably only 1 non-titan will survive round 5. However, if the round 4 game does not come to pass, the titans will never meet in a tournament that is won by a non titan, which then implies that the titans must each loose 2 games apiece to non-titans. Can the titans suffer 4 collective upsets? Of course, but it is quite unlikely. The titans can collectively play at most 13 games and loose the tournament. The first round games are against opponents rated ~800 points below them, and it will cost me 300 prediction points if either of them looses those games. ;-) If a titan looses in round 2, the highest rated opponent he is likely to play in round 3 is rated in the 1600s. Thus is very unlikely that an individual titan will loose in round 2 and in round 3 and be eliminated. Thus, in the first 3 rounds the titans will almost certainly not suffer more than 2 collective defeats. More likely is that at least one titan will remain undefeated and be in the critical game for the final undefeated spot. After round 3 there are at most 7 games left in which to knock out the titans. Collectively, the titans have three advantages: First, they are significantly stronger than non-titans. Fritzlein defeats non-titans at 3/4 or better. 99of9 defeats most non-titans at 2/3 or better. Second, they almost always get to play the weakest players with their tournament record. Third, they only have to play each other in situations where they are very well rewarded for winning. These advantages can be overcome but not 20% of the time. on 11/14/05 at 21:48:04, 99of9 wrote:
The main reason I wanted to save this analysis for after round 1 is that the number of possible future pairings become significantly smaller. If any of the round 1 games are upsets, Fritzlein does not play omar in round 2. If exactly one of seeds 3 through 7 is the only upset, 99of9 plays omar in round 2 and Fritzlein plays the winner of the upset. The only way Fritzlein plays PMertens in round 3 is if I survive to round 3 and that has a <20% chance of happening. Otherwise, it is 99of9 who should expect to play the winner of the evenly matched PMertens - Adanac game. Fritzlein most likely will play robinson in round 3. The floating nature of this tournament makes the winner more predictable, and most everything else less predictable. on 11/14/05 at 23:27:42, Fritzlein wrote:
Well, I think the 9 to 1 odds given by the simulations would make a fair bet, but I don’t gamble. |
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Title: Re: 2006 World Championship Post by 99of9 on Nov 15th, 2005, 4:32am You've made some very good points that I hadn't considered. And I also realise that I'd misinterpreted the way the pairings would work out. I presumed the first 4 rounds were exactly like a knockout tree, but you're right that the sliding means that upsets make the pairings less predictable. |
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Title: Re: 2006 World Championship Post by PMertens on Nov 15th, 2005, 5:03am by the way: I am officially impressed by that analysis ... but I still want to win ;D |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 15th, 2005, 9:03am on 11/15/05 at 02:17:04, Ryan_Cable wrote:
I hadn't considered the significance of this. The seeding does keep me away from 99of9, and I couldn't be happier about that. Yet if I'm not mistaken, we can meet twice without playing for the title. Consider the "Achilles heel" scenario: In round four 99of9 plays me for the for the privelege of the round five bye, and and wins. Going into round six, we could have 99of9 undefeated and Adanac and myself with one loss. I would get the round six bye, but then if Adanac beats 99of9 in round six, I would have to play 99of9 in round seven. It could happen that 99of9 beats me a second time, and then loses a second time to Adanac in round eight, and Adanac is the World Champion! I have definitely been hoping that someone else knocks 99of9 out of the tournament, because it sure worked to my advantage last year. Until now I hadn't considered that someone might knock him out only after he has knocked me out! Generally speaking, it isn't so unlikely that 99of9 and I will deal each other two losses in rounds 4 and 7, so only two upsets would be necessary, specifically in rounds 6 and 8. However, if we are each upset in the first three rounds, 99of9 and I couldn't be paired against each other ever unless we met in round 8 for the Championship. If this happens, I plan to claim it was my strategy all along. :) It is interesting to hear speculation that I might be underrated at 2273. I remember that when I crossed 2300 for the first time there were generous comments that I was poised to rise straight to 2400. I made a bet then that I was overrated from botbashing, and would visit 2200 again before seeing 2400. Since that time my rating has been as high as 2342 and as low as 2206, but not crossed either marker. Today I would still bet that I cross 2200 before 2400, not as a 50-50 speculation, but as a moneymaker. |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 15th, 2005, 9:27am By the way, my wife pointed out that the color determination for the first round happens to be alphabetical by username. By my calculation there's only a 1 in 128 chance that could happen randomly. 'fess up, Omar! |
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Title: Re: 2006 World Championship Post by Ryan_Cable on Nov 15th, 2005, 5:16pm on 11/15/05 at 09:03:40, Fritzlein wrote:
You’re right, I missed this possibility. This makes it significantly less of a lock if a titan gets the final undefeated spot. Probably adds another 3 or 4 percentage points to the field’s chances, since a titan being undefeated after round 4 is quite likely. That brings my prediction into line with the simulations 10%. on 11/15/05 at 09:03:40, Fritzlein wrote:
As a spectator, I am hoping to see you and 99of9 meet in round 4, and then again for the title, which together almost forms a best of 3 mini-match. There is probably a >10% chance of seeing 3 battle of the titans games in this tournament. :-) on 11/15/05 at 09:03:40, Fritzlein wrote:
Your bet is almost certainly a winner unless you intentionally inflate your rating. I think 2273 would make a good best guess for your rating with 99of9 at 2200. Looking at your record vs. the sub-titans centered around 2025, it is reasonable to think you outrank them by 250 to 300 points. If adjustments were made to the record to remove learning games, blitz games, etc, the advantage might fall near the bottom of this range, but I doubt it falls much below it. Likewise, I think 99of9’s record suggests he is 125 to 200 points above them. This puts you somewhere around 2300 and 99of9 around 2175. Then comes the question of how to deal with the fact that 99of9 seems to be roughly equal to you at the board. Mathematically, I think this calls for simulated annealing to get around the intransitivity in the ratings, but I don’t think that would produce a result much more meaningful than my just cutting 25 points from your rating and giving it to 99of9. Philosophically, it comes down to the nature of your relationship with 99of9. It could be that there is a 100 to perhaps even 200 point gap in your true-ratings, and 99of9 just outperforms against you like he has by going undefeated against PMertens. Alternatively, it could be that your true-ratings are about equal and 99of9 has just been unlucky/underperformed in a few sub-titan games. The only way to determine which is correct is if another or better yet several other players of 99of9’s strength join Arimaa (or rise from the sub-titan ranks). Short of this all we have is opinions and guesses. Mine is that you are 50 to 125 points above 99of9 in true-rating. Of course, there is also the details of different ratings at different time controls. I have heard rumors that you are undefeated at postal, which would put you 400+ above everyone else. on 11/15/05 at 09:27:42, Fritzlein wrote:
99of9 finds another strategic advantage. :D |
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Title: Re: 2006 World Championship Post by omar on Nov 15th, 2005, 5:50pm on 11/15/05 at 09:27:42, Fritzlein wrote:
You had me scared there for a minute. I just double checked the pairing program and it seems OK. I ran it again a few times and got pairings like this: pick Fritzlein MrBrain pick acheron 99of9 pick jdb Ryan_Cable pick PMertens grey_0x2A pick megamau Adanac pick robinson naveed pick Belbo BlackKnight pick Paul omar pick MrBrain Fritzlein pick acheron 99of9 pick jdb Ryan_Cable pick grey_0x2A PMertens pick megamau Adanac pick naveed robinson pick BlackKnight Belbo pick Paul omar pick MrBrain Fritzlein pick 99of9 acheron pick jdb Ryan_Cable pick PMertens grey_0x2A pick Adanac megamau pick naveed robinson pick BlackKnight Belbo pick Paul omar So I guess it was just a fluke. Im also going to post the pairing script here so we have an official record of what we used. This is the same script that was used in my simulations of FDE. #!/usr/bin/ruby if ARGV[0] == nil print <<EOM; Floating Double Elimination Format variant to format proposed by Karl Juhnke (Fritzlein) see the Arimaa Forum for more details search for "World Championship tournament format" 1) Everyone plays until they have lost two times. At the end of each round, any player who has lost for the second time is eliminated. 2) At the beginning of each round, if an odd number of players remain, a bye must be assigned. The bye goes to the player who has recieved the fewest byes so far, with ties broken in favor fewest losses so far, and further ties broken in favor of highest pre-tournament rating. 3) The players who don't get a bye are paired iteratively as follows: Select the unpaired player with the fewest losses (ties broken by highest pretournament rating), and pair him with the player in the field he has played the least number of times, with ties broken in favor of having fewest losses, and further ties broken in favor of lower pre-tournament rating. 4) Within each pairing, whoever has played Gold a smaller percentage of times so far in the tournament should get to play Gold for that game, with ties broken randomly. EOM exit; end pa, ga, ra, ph, rn = getTournState(ARGV[0]); if (pa.length == 0) print "done\n" exit end # Determine number of loses for each player # field called 'loses' is set in the player record for x in 0 ... pa.length pa[x]['loses'] = 0 #print " #{pa[x]['n']} #{pa[x]['r']} \n" end for x in 0 ... ga.length e = '' if ga[x]['w'] == ga[x]['1'] e = ga[x]['2'] else e = ga[x]['1'] end if e == "BYE"; next; end pa[ph[e]['loses'] += 1 end # Eliminate players who have lost 3 times pa.delete_if {|x| x['loses'] >= 2} # also re-generate the player name index ph.clear for x in 0 ... pa.length ph[pa[x]['n'] = x end # Used for testing; can be commented out mpa = pa mpa.sort! {|x,y| y['r'] <=> x['r']} print "# player rating loses\n"; for x in 0 ... mpa.length print "* #{mpa[x]['n']} #{mpa[x]['r']} #{mpa[x]['loses']}\n" end print "\n" # If only one player is left then show the winner if (pa.length == 1) if ra[1] != nil print "done\n" exit end print "result #{pa[0]['n']} 1\n" exit end print "* Round #{rn+1}\n" print matchPlayers(pa, ga, ph) exit; BEGIN{ def val(v=0) if v==nil; return 0 end if v==""; return 0 end return v end def matchPlayers(pa=[], ga=[], ph=Hash.new) m = "" # Determine how many times each player has played another # also count number of byes and times played as first player v = Hash.new byes = Hash.new first = Hash.new gamesplayed = Hash.new i = 0 for i in 0 ... ga.length p1 = ga[i]['1'] p2 = ga[i]['2'] v[p1+p2] = val(v[p1+p2]) + 1 v[p2+p1] = val(v[p2+p1]) + 1 first[p1] = val(first[p1]) + 1 if p2 == 'BYE'; byes[p1] = val(byes[p1]) + 1 end if p2 != 'BYE' gamesplayed[p1] = val(gamesplayed[p1]) + 1 end if p1 != 'BYE' gamesplayed[p2] = val(gamesplayed[p2]) + 1 end end # Setup the scores for ordering the players later # score - is used when pairing the players # bsc - is used when giving a player a bye # fsc - is used when deciding which player plays first # played - is total number of games played by this player # also mark that they have not been paired for i in 0 ... pa.length pa[i]['score'] = sprintf("%03d%08d", 99 - val(pa[i]['loses']), pa[i]['r']) pa[i]['bsc'] = sprintf("%03d%03d%08d", 99-val(byes[pa[i]['n']), 99-val(pa[i]['loses']), pa[i]['r']) pa[i]['fsc'] = val(first[pa[i]['n']) pa[i]['played'] = val(gamesplayed[pa[i]['n']) pa[i]['paired'] = 0 end # Order the players by fewest loses and highest ratings pa.sort! {|x,y| y['score'] <=> x['score']} # also re-generate the player name index ph.clear for i in 0 ... pa.length ph[pa[i]['n'] = i end # Give one of the players a bye if there are odd number of players if pa.length % 2 == 1 bpa = pa.sort {|x,y| y['bsc'] <=> x['bsc']} p1 = bpa[0]['n'] m = m + "pick #{p1} BYE\n" pa[ph[p1]['paired'] = 1; end # Now pair the players for i in 0 ... pa.length p1 = pa[i] if p1['paired'] != 0; next end op = [] for j in i+1 ... pa.length p2 = pa[j] if p2['paired'] != 0; next end p2['nsc'] = sprintf("%03d%03d%08d", 99 - val(v[p1['n']+p2['n']), 99 - val(p2['loses']), 9999999 - p2['r']) op.push(p2) end op.sort! {|x,y| y['nsc'] <=> x['nsc']} p2 = op[0] p1['paired'] = 1 p2['paired'] = 1 if (p1['fsc']/(p1['played']+1)) < (p2['fsc']/(p2['played']+1)) m = m + "pick #{p1['n']} #{p2['n']}\n" elsif p2['fsc'] < p1['fsc'] m = m + "pick #{p2['n']} #{p1['n']}\n" else if rand(2)>0 m = m + "pick #{p1['n']} #{p2['n']}\n" else m = m + "pick #{p2['n']} #{p1['n']}\n" end end end return m end def shuffle!(a=[]) x = a.length if x < 2 return end for n in 1 .. 5*x p1 = rand(x) p2 = rand(x) a[p1], a[p2] = a[p2], a[p1] end end # General tournament routines def getTournState(tf) p, g, w = [], [], [] i = Hash.new round = 0 l = IO.readlines(tf) l.each do |x| # read the player if x =~ /^player +(\w+) +(\d+)/ r = Hash.new r['n'], r['r'] = $1, $2.to_i p.push(r) i[$1] = p.length - 1 end # read the game if x =~ /^(pair|pick) +(\w+) +(\w+) winner +(\w+) *(\w*)/ r = Hash.new r['1'], r['2'], r['w'] = $2, $3, $4 if $5 != nil r['d'] = [$4,$5].join(" ") end g.push(r) end # read the result if x =~ /^result +(\w+) *(\w*)/ w[$2.to_i] = $1 end if x =~ /^done$/ break; end # read the player properites we set if x =~ /^\* +set +player +(\w+) +(\w+) +(\w+)/ if i[$1] != nil p[i[$1][$2] = $3 end end # read the round number if x =~ /^\* Round +(\d+)/i round = $1.to_i end end return p, g, w, i, round end def printPlayerProp(p, k, v) print "* set player #{p} #{k} #{v}\n" end def printPlayersProp(p, k) p.each do |r| print "* set player #{r['n']} #{k} #{r[k]}\n" end end } exit |
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Title: Re: 2006 World Championship Post by 99of9 on Nov 15th, 2005, 6:37pm on 11/15/05 at 17:16:20, Ryan_Cable wrote:
Actually I was disappointed to get gold in the first round, because it means I get less gold later. But I do like having my name at the top of the players online list :-) ... except when 6sense is around. |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 15th, 2005, 7:14pm on 11/15/05 at 17:50:55, omar wrote:
That's funny. I guess there was also a 1 in 128 chance it would appear to be ordered by rating, and a 1 in 128 it would appear to be ordered by nationality, and a 1 in 128 chances it would appear to be orded by (fill in the blank). When you consider all the possible correlations one could look for, maybe it isn't so improbable one of them would be true. |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 15th, 2005, 7:26pm on 11/15/05 at 17:16:20, Ryan_Cable wrote:
Aha, another convert to the non-transitivity of ratings! It really opens things up when you stop believing in the mathematical model behind the ratings. What then can a rating mean? What then should a rating mean? Let us open a ratings philosophy thread so we can get it all hashed out and ready for Omar to implement a new system next year. One thing about ratings seems clear from experience: the more the contestant mix around who they play against (e.g. when pairings are determined by tournaments rather than by self-selection) the more accurate ratings become. That's yet another reason broad participation in Arimaa tournaments is good for Arimaa. |
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Title: Re: 2006 World Championship Post by omar on Nov 16th, 2005, 5:18pm on 11/15/05 at 19:14:20, Fritzlein wrote:
Ordered by rating is intentional. By nationality is a coincidence. |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 20th, 2005, 7:56pm OK, fifteen folks showed up for their games, so it is now official that this WC has the most participation ever. Also, many of the games were interesting and intense already in the first round. Just seeing how things are going in this tournament so far, I think it is definitely a good idea to have winners play winners and losers play losers. If we didn't pair that way, but instead had something like 1 and 2 seeds reversing and playing 15 and 16 in the second round, it would be less fun for the prediction contest, less fun for the players involved, and simply less fun all around. Whatever way we decide to tweak the pairing system for next year, we should leave this desirable feature intact. We're still on track for this to be the best WC ever, by a wide margin. |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 20th, 2005, 9:31pm Ryan Cable noticed something with regard to color assignments. In round two Grey_0x2A plays Megamau. In round one Megamau had silver. It isn't clear whether that should count or not, since he forfeited, but either way Megamau has played gold zero times. Meanwhile Grey_0x2A has played gold once, i.e. more than Megamau, so either way Grey_0x2A should get silver in round two. All of this is mostly moot if Megamau forfeits again, but it should inspire one to take another look at the pairing code. |
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Title: Re: 2006 World Championship Post by 99of9 on Nov 20th, 2005, 10:58pm Well spotted Ryan. on 11/20/05 at 21:31:44, Fritzlein wrote:
It's very clear to me that it should count as him having played once with silver. That is the opportunity he had - just because he timed out on move 1 doesn't change the colour he had. |
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Title: Re: 2006 World Championship Post by Ryan_Cable on Nov 21st, 2005, 12:53am on 11/20/05 at 22:58:26, 99of9 wrote:
Yes, I think forfeits should be treated exactly like other games. The person who forfeits doesn’t deserve any favors, and the person receiving the forfeit already gets a big privilege in the free advance to the next round. Mostly, I want this because the rules for losses are predictable up to the coin flips, and handling forfeits is otherwise unspecified. The rules state: The director will also make the final decision on matters of pairing and color assignment. So it is David Fotland’s opinion that matters most. If forfeits are not going to be treated like other games, then I think David should at least state in plain English the algorithm that is being used to handle them. (The ruby script is Greek to me; I can’t even find where it is assigning colors. Even if I understood the code, it would probably still be ambiguous, because it is not clear what the inputs are for a forfeit.) Even if megamau forfeits again, it is important to have this worked out to remove the ambiguity and unpredictability in the color assignment for Adanac and grey_0x2A in round 3+. Whatever rule for handling forfeits is chosen, I can’t think of any good reason for megamau to have silver. I think David should override the script and give megamau gold as soon as possible, so grey_0x2A knows what color to prepare for in case megamau does show. PS BlackKnight vs. acheron confirms that gold is not being assigned by alphabetical order, when the percent of previous gold is equal. |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 21st, 2005, 9:49am Speaking of color assignments, I notice that if I play PMertens in round three, one of us will be assigned gold for the third time in a row. However, it doesn't appear possible for someone to be assigned gold for the fourth time in a row in round four. For that to happen, all eight people who played gold in the first round would have had to win. |
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Title: Re: 2006 World Championship Post by omar on Nov 22nd, 2005, 5:57am on 11/20/05 at 21:31:44, Fritzlein wrote:
Thanks for pointing this out guys. It was due to a bug in the code. I've fixed the code. I've also changed the color assignement for Grey_0x2A and Megamau and sent an email to the players. No need to consult David on this since it is not an arbitrary choice or a dispute. Here is the change to the code: if (p1['fsc']/(p1['played']+1)) < (p2['fsc']/(p2['played']+1)) changed to: if (p1['fsc']/(p1['played']+1.0)) < (p2['fsc']/(p2['played']+1.0)) It was using interger division but I was expecting float. By changing the 1 to 1.0 we cause it to use floating point calculations. |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 22nd, 2005, 8:39am on 11/22/05 at 05:57:51, omar wrote:
Thank you, Omar, for fixing that so quickly, and for running the tournament so smoothly in general. You have worked out a fine system, and you stay on top of any problems, which makes it easy for everyone to have a good time. |
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Title: Re: 2006 World Championship Post by omar on Nov 22nd, 2005, 9:03am I really appreciate you guys letting me know when you find problems. Its very hard to avoid mistakes and you know from my games Im very prone to making blunders :-) |
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Title: Re: 2006 World Championship Post by omar on Nov 22nd, 2005, 9:08am The match up for round two looks like there's going to be some really exciting games. I was trying to fill out my predictions, but I just can't seem to decide on some of the games. This round will definitely spread out the contenders for the prediction contest. |
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Title: Re: 2006 World Championship Post by acheron on Nov 22nd, 2005, 5:23pm 6:00am match time. That's just obscene. |
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Title: Re: 2006 World Championship Post by 99of9 on Nov 22nd, 2005, 5:43pm I suggest that next year players are allowed to select times by slots starting 1 hour apart rather than 2 hours apart. Obviously we will have to make ourselves available for 60 instead of 30 slots, and would still need to be available for the length of a full game starting from the nominated time. As we can see with acheron, one hour can make a lot of difference to the suitability of a time (he'd presumeably much rather play 7am than 6am), so I think that extra choice would help us get even more mutually agreeable timeslots. |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 22nd, 2005, 5:52pm on 11/22/05 at 17:23:47, acheron wrote:
Yeah, hard luck. That's the tradeoff for having it truly be a "world" championship, with players in all sorts of time zones. I personally think the internationalism of the server is one of its coolest features. (And incidentally, it makes me furious when U.S. baseball commentators say things like, "The Chicago White Sox are World Champions!" when they didn't play a single Japanese or Korean team. What part of "world" don't they understand?) But anyway, I'm crazy enough about Arimaa that a 6:00 game seems worth getting up for! :-) |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 22nd, 2005, 5:57pm on 11/22/05 at 17:43:06, 99of9 wrote:
I heartily second this suggestion. Already in the first round I could have used the ability to specify down to the hour. As it happened, my opponent was also from the U.S., so it worked out fine, but I can definitely see the utility in being able to select two 7:00 a.m. slots rather than having to pick one 6:00 a.m. slot. |
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Title: Re: 2006 World Championship Post by acheron on Nov 22nd, 2005, 7:06pm Not being able to schedule at all for Sunday afternoons or Mondays is odd too. Sunday afternoon would have been much preferable. |
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Title: Re: 2006 World Championship Post by BlackKnight on Nov 23rd, 2005, 11:34am Yes, that's a strange time. If I'm right, you are in Pacific time?! In case you have time for example your Friday or Saturday evening after 6pm, I had no problem to switch to another match time. |
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Title: Re: 2006 World Championship Post by acheron on Nov 23rd, 2005, 1:28pm That'd be fine if the system allows for it in some fashion. Otherwise, I'll just bite the bullet and set my alarm for 6:00 on Sunday. |
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Title: Re: 2006 World Championship Post by 99of9 on Nov 23rd, 2005, 2:57pm Did you set 6am as one of your "most desired" options? If so, it's worth making use of the 3-level structure. Only put the times you would really like as left-column ticks. |
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Title: Re: 2006 World Championship Post by acheron on Nov 23rd, 2005, 4:48pm Nah, it was on the "don't abuse me with this" setting. I assume BlackKnight and I just had opposite settings is all. |
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Title: Re: 2006 World Championship Post by BlackKnight on Nov 23rd, 2005, 9:23pm Oh, sorry, Saturday will be the Information Theory Day here, but Sunday morning = your Saturday evening will be really no problem for me. If that would be fine with you, maybe we can ask Omar to swap to a different time slot. |
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Title: Re: 2006 World Championship Post by Ryan_Cable on Nov 24th, 2005, 10:07pm The following tables list: probability of as of the start of round 2, additive change from the start of tournament, multiplicative change from the start of tournament. With listed ratings: StDev 0: Fritzlein 0.64386 -0.00878 0.986546948 99of9 . 0.15914 -0.00439 0.973154773 Ryan_Cable 0.09345 0.00386 1.043085166 PMertens 0.03661 0.00183 1.052616446 Adanac . 0.02929 0.00198 1.072500915 robinson 0.02259 0.00300 1.153139357 Belbo . 0.01419 0.00249 1.212820513 omar . 0.00068 0.00019 1.387755102 Paul . 0.00009 -0.00012 0.428571429 BlackKnight 0.0001 -0.00005 0.666666667 naveed . 0 . -0.00001 0 megamau 0 . 0 . #DIV/0! grey_0x2A 0 . 0 . #DIV/0! jdb . 0 . 0 . #DIV/0! acheron 0 . 0 . #DIV/0! MrBrain 0 . 0 . #DIV/0! StDev 50: Fritzlein 0.60458 -0.00718 0.988263371 99of9 . 0.16611 -0.00402 0.97637101 Ryan_Cable 0.10238 0.00296 1.029772682 PMertens 0.04182 0.00294 1.075617284 Adanac . 0.03717 0.00125 1.034799555 robinson 0.02829 0.00205 1.078125 Belbo . 0.01826 0.00225 1.140537164 omar . 0.00113 0.00014 1.141414141 Paul . 0.00019 -0.00025 0.431818182 BlackKnight 0.00007 -0.00014 0.333333333 naveed . 0 . 0 . #DIV/0! megamau 0 . 0 . #DIV/0! grey_0x2A 0 . 0 . #DIV/0! jdb . 0 . 0 . #DIV/0! acheron 0 . 0 . #DIV/0! MrBrain 0 . 0 . #DIV/0! StDev 100: Fritzlein 0.52139 -0.00689 0.986957674 99of9 . 0.17046 -0.00712 0.959905395 Ryan_Cable 0.11682 0.00168 1.014590933 PMertens 0.05800 0.00268 1.048445409 Adanac . 0.05186 0.00127 1.025103775 robinson 0.04359 0.00368 1.092207467 Belbo . 0.03278 0.00498 1.179136691 omar . 0.00347 0.00061 1.213286713 Paul . 0.00105 -0.00043 0.709459459 BlackKnight 0.00054 -0.00043 0.556701031 naveed . 0.00002 -0.00001 0.666666667 megamau 0.00002 0 . 1 grey_0x2A 0 . 0 . #DIV/0! jdb . 0 . -0.00002 0 acheron 0 . 0 . #DIV/0! MrBrain 0 . 0 . #DIV/0! StDev 200: Fritzlein 0.37380 0.00092 1.002467282 99of9 . 0.17104 0.00100 1.005880969 Ryan_Cable 0.13197 0.00290 1.022468428 PMertens 0.08470 0.00331 1.040668387 Adanac . 0.07989 0.00127 1.01615365 robinson 0.06969 0.00070 1.010146398 Belbo . 0.06007 0.00230 1.039813052 omar . 0.01638 0.00027 1.016759777 Paul . 0.00546 -0.00564 0.491891892 BlackKnight 0.00490 -0.00459 0.516332982 naveed . 0.00082 -0.00123 0.4 megamau 0.00060 -0.00067 0.472440945 grey_0x2A 0.00040 -0.00030 0.571428571 jdb . 0.00025 -0.00020 0.555555556 acheron 0.00003 -0.00003 0.5 MrBrain 0 . -0.00001 0 With me @ 1800, omar +100, and 99of9 +50: StDev 0: Fritzlein 0.59501 -0.01556 0.97451 99of9 . 0.27626 0.00135 1.00491 Ryan_Cable 0.00058 -0.00001 0.98305 PMertens 0.04081 0.00240 1.06248 Adanac . 0.03317 0.00232 1.07520 robinson 0.03218 0.00660 1.25801 Belbo . 0.01582 0.00187 1.13405 omar . 0.00601 0.00122 1.25469 Paul . 0.00009 -0.00015 0.375 BlackKnight 0.00007 -0.00004 0.63636 naveed . 0 . 0 . #DIV/0! megamau 0 . 0 . #DIV/0! grey_0x2A 0 . 0 . #DIV/0! jdb . 0 . 0 . #DIV/0! acheron 0 . 0 . #DIV/0! MrBrain 0 . 0 . #DIV/0! StDev 50: Fritzlein 0.56549 -0.01622 0.97211 99of9 . 0.27747 -0.00110 0.99605 Ryan_Cable 0.00108 0.00033 1.44 PMertens 0.04827 0.00376 1.08447 Adanac . 0.04077 0.00440 1.12097 robinson 0.03792 0.00584 1.18204 Belbo . 0.01991 0.00160 1.08738 omar . 0.00878 0.00192 1.27988 Paul . 0.00013 -0.00040 0.24528 BlackKnight 0.00017 -0.00011 0.60714 naveed . 0.00001 -0.00002 0.33333 megamau 0 . 0 . #DIV/0! grey_0x2A 0 . 0 . #DIV/0! jdb . 0 . 0 . #DIV/0! acheron 0 . 0 . #DIV/0! MrBrain 0 . 0 . #DIV/0! StDev 100: Fritzlein 0.50177 -0.01208 0.97649 99of9 . 0.27045 -0.00313 0.98855 Ryan_Cable 0.00233 -0.00014 0.94331 PMertens 0.06410 0.00407 1.06779 Adanac . 0.05499 0.00224 1.04246 robinson 0.05310 0.00678 1.14637 Belbo . 0.03420 0.00175 1.05392 omar . 0.01736 0.00181 1.11639 Paul . 0.00098 -0.00074 0.56976 BlackKnight 0.00065 -0.00049 0.57017 naveed . 0.00003 -0.00003 0.5 megamau 0.00004 0.00003 4 grey_0x2A 0 . -0.00004 0 jdb . 0 . -0.00003 0 acheron 0 . 0 . #DIV/0! MrBrain 0 . 0 . #DIV/0! With me @ 1800, omar +100, and 99of9 +75: StDev 0: Fritzlein 0.55856 -0.01232 0.97841 99of9 . 0.32908 0.00062 1.00188 Ryan_Cable 0.00051 0.00005 1.10869 PMertens 0.03423 0.00007 1.00204 Adanac . 0.02995 0.00341 1.12848 robinson 0.02880 0.00607 1.26704 Belbo . 0.01378 0.00156 1.12765 omar . 0.00489 0.00069 1.16428 Paul . 0.00013 -0.00011 0.54166 BlackKnight 0.00007 -0.00003 0.7 naveed . 0 . 0 . #DIV/0! megamau 0 . -0.00001 0 grey_0x2A 0 . 0 . #DIV/0! jdb . 0 . 0 . #DIV/0! acheron 0 . 0 . #DIV/0! MrBrain 0 . 0 . #DIV/0! StDev 50: Fritzlein 0.53198 -0.01619 0.97046 99of9 . 0.32650 0.00163 1.00501 Ryan_Cable 0.00077 -0.00010 0.88505 PMertens 0.04430 0.00351 1.08605 Adanac . 0.03649 0.00312 1.09349 robinson 0.03370 0.00569 1.20314 Belbo . 0.01819 0.00153 1.09183 omar . 0.00771 0.00103 1.15419 Paul . 0.00022 -0.00013 0.62857 BlackKnight 0.00013 -0.00010 0.56521 naveed . 0 . 0 . #DIV/0! megamau 0 . 0 . #DIV/0! grey_0x2A 0.00001 0.00001 #DIV/0! jdb . 0 . 0 . #DIV/0! acheron 0 . 0 . #DIV/0! MrBrain 0 . 0 . #DIV/0! StDev 100: Fritzlein 0.47452 -0.01821 0.96304 99of9 . 0.31411 0.00002 1.00006 Ryan_Cable 0.00231 0.00019 1.08962 PMertens 0.05872 0.00249 1.04428 Adanac . 0.05207 0.00472 1.09968 robinson 0.05000 0.00716 1.16713 Belbo . 0.03113 0.00277 1.09767 omar . 0.01594 0.00232 1.17033 Paul . 0.00062 -0.00085 0.42176 BlackKnight 0.00058 -0.00050 0.53703 naveed . 0 . -0.00005 0 megamau 0 . -0.00003 0 grey_0x2A 0 . -0.00001 0 jdb . 0 . -0.00002 0 acheron 0 . 0 . #DIV/0! MrBrain 0 . 0 . #DIV/0! With me @ 1800, omar +100, and 99of9 +100: StDev 0: Fritzlein 0.51804 -0.00870 0.98348 99of9 . 0.38224 -0.00164 0.99572 Ryan_Cable 0.00049 0.00015 1.44117 PMertens 0.03178 0.00099 1.03215 Adanac . 0.02647 0.00281 1.11876 robinson 0.02388 0.00363 1.17925 Belbo . 0.01226 0.00188 1.18111 omar . 0.00466 0.00090 1.23936 Paul . 0.00013 0.00001 1.08333 BlackKnight 0.00005 -0.00002 0.71428 naveed . 0 . -0.00001 0 megamau 0 . 0 . #DIV/0! grey_0x2A 0 . 0 . #DIV/0! jdb . 0 . 0 . #DIV/0! acheron 0 . 0 . #DIV/0! MrBrain 0 . 0 . #DIV/0! StDev 50: Fritzlein 0.49571 -0.01584 0.96903 99of9 . 0.37709 0.00151 1.00402 Ryan_Cable 0.00069 -0.00001 0.98571 PMertens 0.03951 0.00328 1.09053 Adanac . 0.03236 0.00270 1.09103 robinson 0.03146 0.00608 1.23955 Belbo . 0.01589 0.00077 1.05092 omar . 0.00697 0.00173 1.33015 Paul . 0.00019 -0.00013 0.59375 BlackKnight 0.00013 -0.00006 0.68421 naveed . 0 . -0.00003 0 megamau 0 . 0 . #DIV/0! grey_0x2A 0 . 0 . #DIV/0! jdb . 0 . 0 . #DIV/0! acheron 0 . 0 . #DIV/0! MrBrain 0 . 0 . #DIV/0! StDev 100: Fritzlein 0.45188 -0.01143 0.97532 99of9 . 0.35506 -0.00149 0.99582 Ryan_Cable 0.00194 0.00022 1.12790 PMertens 0.05559 0.00318 1.06067 Adanac . 0.04744 0.00364 1.08310 robinson 0.04486 0.00487 1.12178 Belbo . 0.02799 0.00051 1.01855 omar . 0.01403 0.00170 1.13787 Paul . 0.00068 -0.00060 0.53125 BlackKnight 0.00048 -0.00055 0.46601 naveed . 0 . -0.00004 0 megamau 0.00004 0 . 1 grey_0x2A 0.00001 0 . 1 jdb . 0 . -0.00001 0 acheron 0 . 0 . #DIV/0! MrBrain 0 . 0 . #DIV/0! The probabilities didn’t change much from round 1, since there were no upsets. (Additively) Fritzlein lost ~1.5%, since he had a good chance of getting to play the winner of a round 1 upset. robinson gained ~0.6% due to my win over jdb, and virtually all of the rest goes to the undefeated sub-titans. jdb probably took a huge multiplicative hit to his chances, but it vanishes into the noise. The other losers seem to have suffered a ~50% multiplicative decrease in their chances. I also calculated the probability density of upsets for round 2 (counting robinson as a favorite): 0 0.08039 1 0.25946 2 0.33456 3 0.22272 4 0.083008 5 0.017639 6 0.0020765 7 0.00012352 8 0.0000028689 Expectation 2.03035 If megamau forfeits then the probability density becomes: 0 0.14352 1 0.35050 2 0.32204 3 0.14474 4 0.034532 5 0.0043738 6 0.00027253 7 0.0000065225 Expectation 1.59050 Note that none of this implies that one should predict 2 upsets or any upsets for that matter. Your expected absolute score is always decreased by not predicting for the person you believe has >=50% chance of winning. I disclaim any and all responsibility for anyone who uses any of my numbers and/or statements to make predictions! PS Omar, have you heard anything from megamau? |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 25th, 2005, 12:24pm So if there were expected to be 2.03 upsets, and there have been two upsets already, there is only a three percent chance of another upset. I should bet 100% on the favorites in all five of the remaining games, right Ryan? ;) |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 25th, 2005, 12:28pm on 11/24/05 at 22:07:45, Ryan_Cable wrote:
Megamau played a game today (Friday) so it looks like good odds he will play on Sunday, giving us a full 16 participants, so that we break the old record by even more. |
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Title: Re: 2006 World Championship Post by omar on Nov 28th, 2005, 5:03pm on 11/22/05 at 17:23:47, acheron wrote:
There is definitely a lot of room to improve the game scheduling system. I coded it up quickly a few years ago and haven't had a chance to really focus on it again. If anyone wants to improve it, I can send you the code. |
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Title: Re: 2006 World Championship Post by BlackKnight on Nov 29th, 2005, 12:50pm I haven't studied all the sophisticated conditions of the pairing algorithm and so I don't know if the following suggestion makes any sense or fits into the system, but I just realized for my next game the color will be Gold and Omar will have Silver. However, our colors so far were S - G and G - S, respectively. So in a Swiss system chess tournament it would be very natural to continue the sequence and get S - G - S and G - S - G, respectively. Even if we are using a different system, it could still make sense to continue the natural sequence. |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 29th, 2005, 5:59pm BlackKnight, I think that it would fit into the system perfectly well to say "Whoever has played Gold a lower percentage of games so far gets to play Gold. In case of a tie, whoever last played Silver in a round where his opponent played Gold gets to play Gold. Further ties are broken randomly." On the other hand, even though this rule works within the system and does what you want, I'm not sure I like it. Wouldn't it make more sense to assign colors to a player in the order G-S-S-G-G-S-S or S-G-G-S-S-G-G than alternating? If you alternate, then getting Gold in the first round determines your fate much deeper into the tournament, in that you will either play more Gold than Silver or you will get equal numbers. The way it is now, with ties broken randomly, there is no advantage or disadvantage in the later rounds based on the order in which colors were assigned in earlier rounds. I don't think it makes much difference one way or the other, but I have a slight preference for it being random, and if it isn't random, I have a slight preference for "first one and second two" rather than "alternating" as a tiebreaker. That is to say, if we introduce a tiebreaker, I'd like the opposite of the one you propose! :P |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 29th, 2005, 6:25pm on 11/28/05 at 17:03:29, omar wrote:
I'd volunteer to work on this, if only to teach myself a little Perl, but what are the criteria of what is best? Here are the criteria I envision: * Assign all game times independently, so that the only time preferences that matter are yours and your opponent's. In particular, you should never be bumped to a different time slot because the best slot is already "taken" by another game. * Of course the actual game time can only come from times where both players overlap. If they overlap at more than one time, the "best" is selected as follows: * If 1 is a favored time, 2 is an OK time, and 3 is a barely acceptable time, then the rank of the (unordered) pairs of preferences, from best to worst, is (1,1), (1,2), (2,2), (1,3), (2,3), (3,3) * If more than one time slot has a preference pair in the best class, then each such time slot is equally likely to be chosen. For example, if there are only four overlapping times, and the (ordered) pairs of preferences for those are (1,3), (3,1), (3,1), (2,3), then the last time slot is thrown out, and each of the first three is equally likely to become the scheduled game time. One could argue that if it has to be a (3,1) or a (1,3) then each player should have an equal chance of being unhappy, but I disagree. Someone who puts down more 1's as preferences should have a higher chance of one of those slots becoming the actual game time than someone who puts down fewer 1's. Also it seems clear to me that if the time slots have preferences (1,3), (3,1), (3,1), (2,2), then even though the sum is four in each pair, the (2,2) should automatically be selected for fairness sake. These are just thoughts off the top of my head, though. Are there important criteria I am missing? |
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Title: Re: 2006 World Championship Post by 99of9 on Nov 29th, 2005, 7:05pm That seems ok to me. It's also important to include Omar's rule about allocating from Sunday backwards. That way we can fill out our 30 slots with Wednesday sessions that (hopefully) won't be required. Either that or include a 4th category of badness. Or even a 5th... No reason not to record quite detailed gradations of preferences, just like more detailed gradations of time. |
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Title: Re: 2006 World Championship Post by Janzert on Nov 29th, 2005, 8:20pm on 11/29/05 at 18:25:16, Fritzlein wrote:
From a spectator point of view, I would prefer the first rule to only apply for the first two steps. If there are multiple time slots that are equally agreeable to both players it would then be nice if they could be chosen to not overlap with another game. Also choosing the game time seems to be equivalent to a vote involving a large number of candidates (time slots) and two voters (the players). There is actually a fair amount of voting theory out there that should be applicable (http://en.wikipedia.org/wiki/Voting_methods). The current system would seem to be a type of range voting (http://en.wikipedia.org/wiki/Range_voting). Janzert |
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Title: Re: 2006 World Championship Post by 99of9 on Nov 29th, 2005, 9:19pm on 11/29/05 at 20:20:41, Janzert wrote:
Ha, fascinating. As a spectator I prefer the opposite. I would prefer to have a few games going at once so when one gets boring I can focus on the other. That way I use less hours spectating too. |
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Title: Re: 2006 World Championship Post by BlackKnight on Nov 29th, 2005, 11:45pm on 11/29/05 at 17:59:05, Fritzlein wrote:
Thanks for your explanations! Now I see that elimination makes actually a big difference in the system. So I wouldn't like any of those two fixed color assignments that might determine my fate from the first round on. ;) Thus, I also vote for random now! :) |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 30th, 2005, 9:50am on 11/29/05 at 19:05:14, 99of9 wrote:
Interesting. I didn't know that the slots were filled from Sunday backwards. I thought the preponderance of weekend games was explained by the expressed preferences of the players. Personally, I don't necessarily prefer weekend times. A weekend "3" is just as bad as a weekday "3" for me. Last week, in fact, I was travelling the whole weekend, and was quite eager for a Tuesday evening or Wednesday time. It seems to me that we should let the expressed preferences speak for themselves, and not assume that later is better, unless there is some other reason for this I don't see. If we were to add a fourth category of preference, would you agree that the order from best to worst should be (1,1), (1,2), (2,2), (1,3), (2,3), (3,3), (1,4), (2,4), (3,4), (4,4)? That is to say, even though the sum of (1,4) expresses a higher average preference than (3,3), we avoid assigning a superbad slot to anyone if at all possible? |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 30th, 2005, 10:29am on 11/29/05 at 20:20:41, Janzert wrote:
It makes sense to me to apply yet another criteria at the last level, rather than randomly breaking ties between games of equal preferences. Why be random if there is a sensible tiebreaker? On the other hand, I am ambivalent as a spectator. Overlapping games means fewer hours I have to spend watching, and more excitement during those hours. On the other hand, a single game can take up my whole attention when it gets exciting, and I might miss whatever is happening in a concurrent game. Maybe we need to hear from more people about their preferences on this score. Now that I think about it, however, I'm going to contradict my previous post, and say that "later is better" makes a lot of sense as a final tiebreaker, because whatever the preferences of the participants, spectators are more likely to be able to watch a game if it is on the weekend. |
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Title: Re: 2006 World Championship Post by Adanac on Nov 30th, 2005, 11:39am on 11/30/05 at 10:29:04, Fritzlein wrote:
I like the idea of concurrent games on the weekends. It's easier to plan my schedule around spectating if the games are clumped together and it shouldn't be too difficult to follow 2 games simultaneously. It would also allow potential start times every hour, rather than every 2 hours (convenient!) and it could accomodate future tournaments with 24 or 32 players. Also, we could more easily justify 2-3 minutes per move rather than 90 seconds if the spectators potentially have 2 games to watch. |
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Title: Re: 2006 World Championship Post by MrBrain on Nov 30th, 2005, 4:28pm I dislike the "later" criterion because my weekends are almost always extremely busy. The only time that really worked for me this week was Tuesday, but I still ended up with a 1 am draw on the weekend. |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 30th, 2005, 4:46pm According to pre-tournament ratings, the third round features 1 vs. 6 and 2 vs. 5, but I just noticed that according to current ratings it is actually 1 vs. 4 and 2 vs. 3. This seems like an argument that the floating pairings are working well. I confess to being thrilled that my nemesis, 99of9, has to play against his nemesis Adanac in the third round. If Adanac wins, then I can't be paired against 99of9 before round seven, even if I lose once myself. |
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Title: Re: 2006 World Championship Post by 99of9 on Nov 30th, 2005, 5:14pm on 11/30/05 at 16:46:57, Fritzlein wrote:
I suppose I should try to win then! |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 30th, 2005, 5:54pm on 11/30/05 at 16:28:33, MrBrain wrote:
Well, if I'm not the only one who dislikes the "later is better" criterion, then I suggest we scrap it entirely, and simply choose randomly between times of equal preference. It seems unfair to people who prefer weekday times to offer such times but then bias the scheduling towards the weekend. But in any case, if we switch to the finer granularity of one hour time slots and four or five levels of preference, then the preferences themselves should do better at unambiguously determining the best time. It may become superfluous to make assumptions on behalf of the players about what is best for them. |
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Title: Re: 2006 World Championship Post by 99of9 on Nov 30th, 2005, 6:21pm on 11/30/05 at 17:54:16, Fritzlein wrote:
Yes, I think this is the best solution. I think at least 5 different levels of preference is probably normal for most people. For example: 1) These times are ideal for me, no drawbacks. 2) Times like this would make a particular day busy, but there's no actual clash. 3) I can play these times, but I may be slightly tired and may not play at my best. 4) I would need reschedule other committments in order to play at these times. 5) This is in the middle of the night. I am available, but would otherwise be sleeping! I also agree with how you were proposing to order pairs Fritz. But I do wonder if there's a slightly more mathematical way of treating cases where one person has only made a few slots available at that level, whereas the other has put up lots of options. I'll try to think of something and come back to this (or look up the voting systems that were mentioned). (Because under your system one person could effectively veto most times by proposing level 1 for limited set of slots, and level 5 for all the rest of his/her 30. It would be quite unfair if that was encouraged by the system.) |
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Title: Re: 2006 World Championship Post by 99of9 on Nov 30th, 2005, 6:48pm Now that I think a little longer, perhaps it would be sufficient to make a rule that everyone needs to choose at least 5 slots of type 1, at least 10 of type 2 or higher, at least 15 of type 3 or higher, at least 20 of type 4 or higher, and obviously at least 30 of type 5 or higher. (double this if the number of slots is doubled) |
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Title: Re: 2006 World Championship Post by Fritzlein on Nov 30th, 2005, 7:23pm on 11/30/05 at 18:21:32, 99of9 wrote:
I didn't think about this problem. I'm not sure how bad it is, though. If you put most of your slots at the lowest preference, then you are really gambling. If it happens that none of your few top preferences overlaps with my available times, then my preferences will completely control the choice among the slots that do overlap. This could stick you with a hideous time when you could have had one that is merely bad. Therefore, I'm not convinced my system does encourage putting all your eggs in one basket. Yes, it would give you a better chance of getting your most preferred slot, but also a better chance chance of getting your least preferred slot. If I understand the sentiment that has been expressed on this topic, people are more worried about avoiding a handful of awful times than they are worried about securing a particularly good time. Someone who has to pick four terrible times just to round out the thirty would be well advised to set only those four at the lowest preference. We could require everyone to select exactly 1/5 of each of the five categories. I suspect that most of the time this would actually be forcing people to act in their own best interest. The related game theory would be fascinating. On the other hand, there might be rare cases where an extreme assignment of preferences reflects reality, in which case it would be too bad to forbid players from making the relevant choices. I would merely advise players that it is probably wisest to spread out over the categories, and I wouldn't impose any restrictions. Remember, there will still be times the players overlap only in one slot, and that slot happens to be terrible for both players, or terrible for one and perfect for the other. Because bad situations and unfair situations can't be avoided entirely, we should temper our enthusiasm for complicating the current scheme. We may end up putting in a lot of effort for only a little benefit. :-/ |
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Title: Re: 2006 World Championship Post by 99of9 on Nov 30th, 2005, 7:58pm [EDIT: Fritz's recent post came in as I was typing this one up. I agree with most of his sentiments therein.] on 11/30/05 at 19:23:55, Fritzlein wrote:
Of course you are right, but my feeling is it is worth making at least some of the changes, especially the easy ones. Doubling the number of timeslots and increasing the number of preference gradations seems like it would be easy. Perhaps we just "request" that people provide an even distribution, rather than trying to enforce it in software. My feeling comes from the fact that as an Australian I am perhaps the least likely to fit in with everyone else's natural timezone preferences. Despite this, and despite being unable to choose a full 30 slots on any of the 3 weeks, I have been reasonably satisfied with the timeslots I got. This week's is the worst, when I have to start a game at 11pm on a Saturday night before flying interstate on Sunday. Obviously that's still not too bad. The point is, that although we can't mathematically guarantee good overlaps, from a statistical standpoint reasonable overlaps are likely if both players supply 30 choices. |
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Title: Re: 2006 World Championship Post by Ryan_Cable on Dec 1st, 2005, 4:49am 1 Fritzlein 2273 2 99of9 . 2142 3 Ryan_Cable 2105 4 PMertens 2045 5 Adanac . 2039 6 robinson 2026 7 Belbo . 2009 8 omar . 1860 9 BlackKnight 1818 10 megamau 1651 11 jdb . 1584 12 MrBrain 1369 The following tables list: probability of as of the start of round 3, additive change from the start of tournament, multiplicative change from the start of tournament, additive change from last round, multiplicative change from last round. With me @ 1800, omar +100, and 99of9 +75: StDev 0: Fritzlein 0.56991 -0.00097 0.99830 0.01135 1.020320109 99of9 . 0.33813 0.00967 1.02944 0.00905 1.027500912 Ryan_Cable 0.00043 -0.00003 0.93478 -0.00008 0.843137255 PMertens 0.02101 -0.01315 0.61504 -0.01322 0.613789074 Adanac . 0.03317 0.00663 1.24981 0.00322 1.107512521 robinson 0.02614 0.00341 1.15002 -0.00266 0.907638889 Belbo . 0.00857 -0.00365 0.70130 -0.00521 0.62191582 omar . 0.0025 -0.00170 0.59523 -0.00239 0.511247444 BlackKnight 0.00014 0.00004 1.4 . 0.00007 2 megamau 0 . -0.00001 0 . 0 . #DIV/0! jdb . 0 . 0 . #DIV/0! 0 . #DIV/0! MrBrain 0 . 0 . #DIV/0! 0 . #DIV/0! StDev 50: Fritzlein 0.54837 0.00020 1.00036 0.01639 1.030809429 99of9 . 0.34058 0.01571 1.04835 0.01408 1.043124043 Ryan_Cable 0.00067 -0.00020 0.77011 -0.00010 0.87012987 PMertens 0.02399 -0.01680 0.58813 -0.02031 0.541534989 Adanac . 0.04047 0.00710 1.21276 0.00398 1.109070978 robinson 0.03170 0.00369 1.13173 -0.00200 0.940652819 Belbo . 0.01064 -0.00602 0.63865 -0.00755 0.584936778 omar . 0.00346 -0.00322 0.51796 -0.00425 0.448767834 BlackKnight 0.00011 -0.00012 0.47826 -0.00002 0.846153846 megamau 0.00001 0.00001 #DIV/0! 0.00001 #DIV/0! jdb . 0 . 0 . #DIV/0! 0 . #DIV/0! MrBrain 0 . 0 . #DIV/0! 0 . #DIV/0! StDev 100: Fritzlein 0.50146 0.00873 1.01771 0.02694 1.05677316 99of9 . 0.33179 0.01770 1.05635 0.01768 1.056286014 Ryan_Cable 0.00141 -0.00071 0.66509 -0.00090 0.61038961 PMertens 0.03304 -0.02319 0.58758 -0.02568 0.5626703 Adanac . 0.05913 0.01178 1.24878 0.00706 1.13558671 robinson 0.04811 0.00527 1.12301 -0.00189 0.9622 Belbo . 0.01707 -0.01129 0.60190 -0.01406 0.548345647 omar . 0.00738 -0.00624 0.54185 -0.00856 0.462986198 BlackKnight 0.00058 -0.00050 0.53703 0 . 1 megamau 0.00003 0 . 1 . 0.00003 #DIV/0! jdb . 0 . -0.00002 0 . 0 . #DIV/0! MrBrain 0 . 0 . #DIV/0! 0 . #DIV/0! I have cut the number of simulation results that I am listing to save myself the effort of formatting them. The 99of9 +50 sims reduced 99of9 ~5% and increased Fritzlein ~4%. The 99of9 +100 sims increased 99of9 ~6% and reduced Fritzlein ~4%. On the whole, little has changed since the beginning of the tournament, since there have been no titan upsets. Fritzlein has come back to where he was at the beginning of the tournament, and 99of9 has gained (additively) ~1.3%. The undefeated sub-titans (Adanac and robinson) have gained (additively) 1% total. Most of these points have come at the expense of PMertens, with Belbo and omar making smaller losses. The eliminated players never had much chance of winning. One slightly strange result is that robinson lost (multiplicatively) ~7%, since the last round, despite winning; I think this comes from the lack of a titan upset. The probability density of upsets for round 2: 0 0.31449 1 0.41612 2 0.21079 3 0.051735 4 0.0064502 5 0.00038965 6 0.0000090180 Expectation 1.02072 |
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Title: Re: 2006 World Championship Post by MrBrain on Dec 1st, 2005, 7:31am on 11/30/05 at 18:21:32, 99of9 wrote:
Other than Tuesday, this was my situation for this week. |
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Title: Re: 2006 World Championship Post by Fritzlein on Dec 1st, 2005, 8:04am Ryan, Thanks for continuing to post the results of your simulations. To me it feels like beating a tough player like Omar must have boosted my chances significantly, because I now have to survive one round fewer to win it all, but I guess the sims have most of my losses coming to 99of9. Further reinforcement for me to root for Adanac on Saturday. :-) on 12/01/05 at 04:49:18, Ryan_Cable wrote:
My predictions add up to a cumulative 1.65 upsets. It's good to know that I am on the conservative side of things, as I would wish to be when my standing is fairly good. |
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Title: Re: 2006 World Championship Post by Fritzlein on Dec 2nd, 2005, 7:10pm We're two games into the third round, just over half the games have been played, and already the tournament has become a changing of the guard. All three of the medalists from the 2004 championship are out, and two of the three medalists from the 2005 championship are out. There are so many strong Arimaa players around nowadays, "the field" in this tournament is a veritable minefield. I'm quaking in my boots, myself. |
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Title: Re: 2006 World Championship Post by Ryan_Cable on Dec 2nd, 2005, 10:29pm on 12/01/05 at 08:04:41, Fritzlein wrote:
Not really, you actually had a 0.3123 chance of loosing to one of MrBrain, omar + 100, and robinson. Likewise, 99of9 +75 had a 0.4395 chance of loosing once to acheron, Belbo, and Adanac. Thus, the chance of you two meeting in round 4 was 0.3855 (assuming the possibility of different pairings comes out in the wash). Even at round 3, there is only a 0.5928 chance that round 4 will have a battle of the titans. However, a titan is expected to have no trouble beating the bottom of the looser bracket for rounds 2 and 3, and very little trouble in round 4. Thus, the titans are both expected to survive to round 5 (>90%), which creates a focusing effect, where round 5 is likely to have one undefeated titan and one wounded titan. It doesn’t really matter how you get there; the wounded titan takes a big hit in his chances, but all of this must go to the undefeated titan. Only if a titan is eliminated or (less unlikely) a non-titan takes the undefeated spot does the field make significant gains, and still not big gains. Consider, if Adanac beats 99of9, then beats Fritzlein to take the undefeated spot. Then let 99of9 be eliminated, and let Fritzlein survive to face an undefeated Adanac for the title. At this point, Fritzlein would have a 0.6299 chance of winning the tournament!!! If it were 99of9 instead of Fritzlein, he would have a 0.5415 chance of winning! Yet if it were the titan that was undefeated, Adanac would only have a 0.04258 or 0.06976 chance to win. The square of a small fraction is a very small fraction, but the square of a big fraction is still a fairly large fraction. The main advantage of any field is numerical superiority, which was strong enough to make FIDE call Alexander Khalifman and Rustam Kasimdzhanov world champions. But in a 16 player FDE, the focusing effect means that the most intense portion of the tournament comes after the field is likely to have been cut down to just 3 non-titans. on 12/02/05 at 19:10:58, Fritzlein wrote:
And the minefield is covered by nearly impenetrable interlocking fires. ;D |
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Title: Re: 2006 World Championship Post by Fritzlein on Dec 3rd, 2005, 9:30am on 12/02/05 at 22:29:24, Ryan_Cable wrote:
OK, I understand better now what your sims are saying. Quote:
Part of my issue is that I never quite believed the size of the fractions the pre-tournament ratings indicated. Apparently you are simulating me at 80% to beat each of Robinson and Adanac, for about a 64% chance of getting the round 5 bye, but I sure won't be betting that much on myself in the prediction contest. Quote:
Well, we have one "titan" upset now, which means that 99of9 and I can no longer face each other until round seven. While I'm thrilled about that, it is hardly far-fetched that there will be three more such upsets, giving someone else the crown without the "titans" ever having played each other. I'll give myself a slight boost for surviving two rounds, but at best I'm still only 55% to win it all, with say 15% to 99of9 and 30% to the field. Only if I can beat Robinson this round will I boost myself to 65% at the field's expense. |
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Title: Re: 2006 World Championship Post by 99of9 on Dec 3rd, 2005, 3:58pm on 12/03/05 at 09:30:56, Fritzlein wrote:
Adanac should no longer be called field, since he clearly has a greater % than me now. |
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Title: Re: 2006 World Championship Post by Fritzlein on Dec 11th, 2005, 4:17pm Well, so much for the "titans". The "field" is looking pretty strong right now. Indeed, the changing of the guard is complete. The two undefeated players are folks who just learned this year! Well done, Robinson and Adanac. Have fun duking it out for the fifth round bye! |
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Title: Re: 2006 World Championship Post by Janzert on Dec 11th, 2005, 8:41pm I logged into the game room several times over the last couple days and never figured out that the games had been successfully rescheduled yet. :( Oh well, on to the next round. Janzert |
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Title: Re: 2006 World Championship Post by 99of9 on Dec 11th, 2005, 9:33pm We missed some crackers Janzert. I was asleep for most of the games. Better observation next time :-). |
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Title: Re: 2006 World Championship Post by Ryan_Cable on Dec 12th, 2005, 1:28am 1 Fritzlein 2273 2 99of9 . 2142 3 Ryan_Cable 2105 4 PMertens 2045 5 Adanac . 2039 6 robinson 2026 7 BlackKnight 1818 8 megamau 1651 Well, that was an exciting two weeks. Seeds 5 and 6 facing off for the undefeated spot is certainly unexpected. For the first time, we have 4 players with >10% chances, and we are likely to still have 3 players with >10% chances after round 4. While the upsets have quite sensibly received the most comments, it should also be noted that all seeds 6 and above are still in the tournament, and except for me all of them are very likely to still be there after round 4. The remainder of the tournament is going to be about as exciting as is mathematically possible. The following tables list: probability of winning as of the start of round 4, additive change from the start of tournament, multiplicative change from the start of tournament, additive change from last round, multiplicative change from last round. With me @ 1800 and 99of9 +75: StDev 0: Fritzlein 0.43808 -0.13280 0.76737 -0.13183 0.76868 99of9 . 0.27875 -0.04971 0.84865 -0.05938 0.82438 Ryan_Cable 0.00032 -0.00014 0.69565 -0.00011 0.74418 PMertens 0.03909 0.00493 1.14432 0.01808 1.86054 Adanac . 0.13046 0.10392 4.91559 0.09729 3.93307 robinson 0.11298 0.09025 4.97052 0.08684 4.32211 BlackKnight 0.00032 0.00022 3.2 . 0.00018 2.28571 megamau 0 . -0.00001 0 . 0 . #DIV/0! StDev 50: Fritzlein 0.42400 -0.12417 0.77348 -0.12437 0.77320 99of9 . 0.27234 -0.05253 0.83830 -0.06824 0.79963 Ryan_Cable 0.00069 -0.00018 0.79310 0.00002 1.02985 PMertens 0.04312 0.00233 1.05712 0.01913 1.79741 Adanac . 0.13791 0.10454 4.13275 0.09744 3.40770 robinson 0.12139 0.09338 4.33380 0.08969 3.82933 BlackKnight 0.00054 0.00031 2.34782 0.00043 4.90909 megamau 0.00001 0.00001 #DIV/0! 0 . 1 StDev 100: Fritzlein 0.39195 -0.10078 0.79546 -0.10951 0.78161 99of9 . 0.26192 -0.05217 0.83390 -0.06987 0.78941 Ryan_Cable 0.00191 -0.00021 0.90094 0.00050 1.35460 PMertens 0.05339 -0.00284 0.94949 0.02035 1.61592 Adanac . 0.15233 0.10498 3.21710 0.09320 2.57618 robinson 0.13689 0.09405 3.19537 0.08878 2.84535 BlackKnight 0.00143 0.00035 1.32407 0.00085 2.46551 megamau 0.00018 0.00015 6 . 0.00015 6 Adanac and robinson have increased their chances ~4 fold. Yet the titans only take a ~20% multiplicative decrease, with the biggest loss coming from Fritzlein, since he was most likely to be the final undefeated. With my standard ratings estimates, the titans retain a 70% chance of winning the tournament. Raising Adanac to 2114 and robinson to 2131 (their end of round 3 ratings): StDev 0: Fritzlein 0.35121 99of9 . 0.21372 Ryan_Cable 0.00024 PMertens 0.02635 Adanac . 0.18289 robinson 0.22547 BlackKnight 0.00012 megamau 0 StDev 50: Fritzlein 0.34206 99of9 . 0.21006 Ryan_Cable 0.00033 PMertens 0.02954 Adanac . 0.18740 robinson 0.23036 BlackKnight 0.00023 megamau 0.00002 StDev 100: Fritzlein 0.31712 99of9 . 0.20547 Ryan_Cable 0.00120 PMertens 0.03793 Adanac . 0.20133 robinson 0.23595 BlackKnight 0.00098 megamau 0.00002 Now, robinson is actually >1% above 99of9, and Adanac is only 3% behind 99of9. Fritzlein is still 12% above anyone else. The titans are reduced to a 55% chance of winning. Personally, I think the odds are about Fritzlein 41%, 99of9 22%, robinson 18%, Adanac 17%, PMertens 2%. 99of9's main advantage in the tournament was his being slightly better than Fritzlein on the board, and it is now unlikely for there to be even one Battle of the Titans game. The only thing he has left going for him (aside from just the skill that shows up in his rating) is the fact that he is PMertens's Achilles' heal. On the other hand, Fritzlein's strength comes from the fact that he is expected to be able to beat any non-titan 75% of the time, so the loss he suffered is somewhat offset by the loss 99of9 suffered. I think Adanac and robinson are probably about half way between their pre and post ratings at ~2085. PMertens will have to make good on his Houdini nickname to win the tournament. Here is the probability density of upsets for round 4 with me @ 1800 and 99of9 +75: 0 0.36856 1 0.47928 2 0.13997 3 0.011930 4 0.00023389 Expectation 0.79597 With Adanac @ 2114 and robinson @ 2131, counting robinson as the favorite: 0 0.37265 1 0.47672 2 0.13859 3 0.011794 4 0.00023110 Expectation 0.79022 Nearly all of the upset probability comes form the Adanac v. robinson tossup. There is a 0.88399 chance that both titans win, and a 0.71056 chance that there are no loser bracket upsets. Thus it is reasonable to go ahead and run some simulations for round 5 assuming no loser bracket upsets. robinson undefeated with 99of9 +75, Adanac @ 2114 and robinson @ 2131: StDev 0: Fritzlein 0.32348 99of9 . 0.23887 PMertens 0.03140 Adanac . 0.05803 robinson 0.34822 StDev 50: Fritzlein 0.31855 99of9 . 0.23578 PMertens 0.03561 Adanac . 0.06382 robinson 0.34624 StDev 100: Fritzlein 0.30697 99of9 . 0.23197 PMertens 0.04739 Adanac . 0.07918 robinson 0.33449 Adanac undefeated with 99of9 +75, Adanac @ 2114 and robinson @ 2131: StDev 0: Fritzlein 0.37196 99of9 . 0.20700 PMertens 0.02903 Adanac . 0.31068 robinson 0.08133 StDev 50: Fritzlein 0.35945 99of9 . 0.20987 PMertens 0.03391 Adanac . 0.30954 robinson 0.08723 StDev 100: Fritzlein 0.34039 99of9 . 0.21272 PMertens 0.04540 Adanac . 0.30125 robinson 0.10024 There are two likely pairings for round 5: Adanac v. Fritzlein and 99of9 v. PMertens or PMertens v. Fritzlein and 99of9 v. robinson. (There is also a 20% chance I could be in PMertens’s spot.) 99of9 would prefer the former; PMertens and probably Fritzlein would prefer the latter. Collectively the titans are probably better off with robinson taking the undefeated spot, though the simulations say otherwise. There have been 6 upsets in 22 games. 4 of these were in games with a 70%+ favorite. My standard rating estimates expected 4.14676 and 2.22388 respectively. They gave a 0.21056 chance of >=6 upsets and a 0.167998149 chance of >=4 big upsets. Part of this comes from the fact that I did not bother to adjust the ratings of MrBrain and jdb, despite the fact they were known to be underrated before the tournament began. The rest comes from the fact that Adanac and robinson have outperformed their pre-tournament ratings. It is difficult to say how much of this outperformance is due to luck and how much is due to underrating. Still, I think my rating estimates have performed reasonably well so far. |
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Title: Re: 2006 World Championship Post by Fritzlein on Dec 12th, 2005, 9:36am Thanks for the simulations and analysis, Ryan. Even though I think they have overstated my chances and continue to do so (Don't Adanac and Robinson now have a greater chance of winning than 99of9 and I?), I find them very interesting reading. |
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Title: Re: 2006 World Championship Post by Ryan_Cable on Dec 21st, 2005, 6:43am I calculated the exact odds for the tournament. I don’t have time to post the details but the odds are: robinson 0.359618152 Fritzlein 0.322872859 99of9 0.19549511 Adanac 0.091306607 PMertens 0.030707272 Good Luck everyone. |
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Title: Re: 2006 World Championship Post by PMertens on Dec 21st, 2005, 7:10am those simply cannot be correct ... |
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Title: Re: 2006 World Championship Post by 99of9 on Dec 21st, 2005, 7:23am Here's my current estimate: robinson 48% Fritzlein 16% 99of9 15% Adanac 14% PMertens 7% |
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Title: Re: 2006 World Championship Post by Fritzlein on Dec 21st, 2005, 9:04am I have to say my intuition is a lot closer to 99of9's numbers than to Ryan's numbers. Thanks for the tipoff, 99of9, that you are betting 55% on me this round in the prediction contest. ;-) |
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Title: Re: 2006 World Championship Post by 99of9 on Dec 21st, 2005, 4:18pm on 12/21/05 at 09:04:49, Fritzlein wrote:
I included Achilles effects in my estimates, so it's not that simple. |
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Title: Re: 2006 World Championship Post by Fritzlein on Dec 23rd, 2005, 8:11am What a great tournament! There's definitely a new set of titans in town... I certainly wanted to win, but at least after getting eliminated in round five I can take a break from Arimaa and relax with my family over the holidays. |
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Title: Re: 2006 World Championship Post by PMertens on Dec 23rd, 2005, 6:56pm hey, I can do the same :P |
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Title: Re: 2006 World Championship Post by Fritzlein on Dec 25th, 2005, 10:22pm It seems that Adanac's WC victory over me is not showing up in the Player of the Month standings for December. Admittedly, PMertens probably has the PotM victory sewn up at this point, but it is still worth investigating what is wrong with the standings. |
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Title: Re: 2006 World Championship Post by PMertens on Dec 26th, 2005, 5:44am as far as I can tell everything is normal ... you guys already played one game with Adanac gold ... if you would play another with Adanac silver it would count. |
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Title: Re: 2006 World Championship Post by Fritzlein on Dec 26th, 2005, 9:25pm Oh, I forgot about the color issue. Sorry for the red herring. |
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Title: Re: 2006 World Championship Post by omar on Jan 1st, 2006, 11:09am I won't be around to see the finals of the WC games. It's been the most exciting tournament yet. Even more exicting than any professional chess tournament I've ever followed. Good luck to the remaining players. My brother in law Sameer will be setting up the games while Im gone. If you notice he forgot something please send a reminder at babbhai@yahoo.com and mohabbatse@yahoo.com. I should be back on Jan 17th, inshallah. |
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Title: Re: 2006 World Championship Post by Fritzlein on Jan 6th, 2006, 4:04pm on 11/15/05 at 17:16:20, Ryan_Cable wrote:
Well, Ryan, you got your wish. The World Championship will include (and be decided by) a best of 3 mini-match between the titans, because neither of the titans lost any games to non-titans. Of course, the titans are Adanac and Robinson this year, but you can't be faulted for not knowing that in advance... ;-) |
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Title: Re: 2006 World Championship Post by Fritzlein on Jan 13th, 2006, 6:18pm First, congratulations to Robinson, our new World Champion! I don't think we could have a better representative for the game. Arimaa will look all the more alluring to newcomers if an exciting attacking style can win all the marbles. Second, I just have to say again that this has been an incredible tournament. Just a few of the reasons why: * A record sixteen participants * Six different countries represented * Many exciting games that swung back and forth several times * Lots of upsets to keep things interesting * Many different openings and styles of play. (It's astonishing that there is still no single strategy or type of play that has emerged as dominant, nor has any piece setup or opening move sequence become standard.) Congrats again to Omar for creating a great game and great place to play it. Finally, congrats to all of us for taking part. |
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Title: Re: 2006 World Championship Post by omar on Jan 28th, 2006, 10:31am Yes, this definitely was an awsome tournament. Quite unpredictable and full of exciting games. Congratulations to Till for earning the title of Arimaa world champion. Congratulations to Greg for placing second and a big thanks to all the players for entering the tournament and making it such an exiciting and entertaining event. I am convinced now that if Arimaa games of the future continue to be as exciting as those of this tournament, the spectators and fans of Arimaa will find much satisfaction and entertainment in future tournaments. Congratulations to Jeff, Greg and Toby for placing 1st, 2nd and 3rd in the prediction contest. Karl deserves an honorable mention for being so close to the pack of top predictors and well ahead of the rest of the field. |
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